For the computer to assist in the medical diagnosis and treatment processes, a series of systematic mathematical algorithms must be developed that correspond in some sense to the reasoning used by the diagnostician. In terms of the propositional calculus of symbolic logic, the patient presents a symptom profile, G, which is a Boolean function of possible symptoms, either present or absent or undetermined. The diagnosis, which is also a Boolean function, f, of possible diseases, is found from the fundamental formula of medical diagnosis, E → (G → f), where E is the Boolean function representing medical knowledge. An example of an elementary computation is given to illustrate the process of solving the fundamental formula. In cases where complete symptom information is unavailable, the computer can apply Bayes' formula, which correlates the conditional probability of having a disease complex given a certain symptom profile with that of having the given symptom profile given the disease complex and the total probability of the patient's having the disease complex. A simple illustrative example is given of the application of Bayes' formula. An "uncertainty principle" exists in the collection of statistics for determining the total probability, due to the time lag in processing data. A method is given for handling data from patients presenting incomplete symptom profiles. When medical knowledge is so voluminous as to make impractical the recording of all possible symptom-disease combinations, then techniques developed in pattern-recognition studies can be utilized. The least-probable symptom complex will be omitted, and the loss can be compensated for by comparing the patient's given symptom profile with "weighted" possible symptom complexes. Again, an illustrative example is given. After the probabilities for possible alternative diagnoses have been determined, the treatment plan must be determined. We distinguish three basic kinds of problem: 1) treatment decisions under certainty, which involve simple value-theory considerations and linear programming; 2) treatment decisions under risk, where the probabilities of alternative diagnoses are known, which involve optimization of a mathematical expectation; and 3) tr- eatment decisions under uncertainty, where the probabilities of the alternative diagnoses are unknown, which are amenable to the application of "game theory." Such decisions all involve value determinations, which can be broken down into tangible and intangible values. When alternative diagnoses remain, the response of the patient to the treatment chosen is a further symptom, which can be used in reevaluating the diagnosis. In such cases the techniques of dynamic programming may be applied. The problem of determining the transition probabilities of a patient's moving from one state of health to another during a certain course of treatment presents difficulties, and a method for alleviating the problem is presented, utilizing Bayes' formula to process current patient charts instead of relying on past record searches. Conditional probabilities can be further utilized in the comparison of two treatments. Finally, a brief survey is given of applications of computer-diagnosis aids as reported in the literature.